I multiply 3 by 1 to get 3.

And obviously, you can set this equal to 0. The zero vector is a member of V, so any transformation of if you just put a 0 here, you'll get the zero vector.

PHASE TWO D DAY to D 7

Create from scratch

Less than zero.

So we are going to start at 0.

Well, I'm going to start from scratch.

So let's just put zero right over here, since we are taking the distance from 0.

Global Zero at Ground Zero

So delta x approaching 0 is the same exact thing as taking the limit as u approaches 0.

The absolute value is really just the distance of x from 0. distance from 0

That is going to approach 0.

BECAUSE WE ARE STARTlNG AT ZERO

It's getting near zero.

We need to start over from zero.

Bring down this 0 right here.

I didn't work my way up out of there for nothing.

Start again humbly from zero.

Bring down the next zero.

Because if a approaches 0 here, that's going to make x approach 0.

the zero.

As we approach 0, as x approaches 0, this function approaches 1.

So this zero is less than this one, this zero is less than this two, this three is less than this eight.

In these equations, scattering and reflection are considered to be close to zero or otherwise accounted for.

limit as its denominator approaches 0, we're going to make delta x go to 0.

This right here is going to approach 0.

We could try to approach zero.

So, it is not starting from zero.

9 is greater than 0. Check.

If approaches As x approaches 0 here, a is also going to approach 0, right?

I look to the left of that zero and I say well, can I borrow the one from zero?

PHASE THREE D 8 to D 29

PHASE FOUR D 29 to D 60

There are people who would actually let you borrow the one from the zero, but I say no, instead of borrowing the one from the zero,

Hide zero

So that is 0.

Bring down the zero.

Our second derivative is positive as we approach 0 from the left, and it's positive as we approach 0 from the right.

Only if s is greater than zero, when you get a minus infinity here does this approach zero.

Negative 2 cosine of x, for, for x is less than zero. And then for x is greater than zero...

Or you could view it this way as a approaches 0, x is still approaching 0.

But it is equally impossible to start from scratch.

A floating point value, greater than zero

We are starting from scratch.

It can approach zero.